What is the Greatest Common Factor of 27125 and 27132?

Greatest common factor (GCF) of 27125 and 27132 is 7.

GCF(27125,27132) = 7

We will now calculate the prime factors of 27125 and 27132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27125 and 27132.

How to find the GCF of 27125 and 27132?

We will first find the prime factorization of 27125 and 27132. After we will calculate the factors of 27125 and 27132 and find the biggest common factor number .

Step-1: Prime Factorization of 27125

Prime factors of 27125 are 5, 7, 31. Prime factorization of 27125 in exponential form is:

27125 = 5³ × 7¹ × 31¹

Step-2: Prime Factorization of 27132

Prime factors of 27132 are 2, 3, 7, 17, 19. Prime factorization of 27132 in exponential form is:

27132 = 2² × 3¹ × 7¹ × 17¹ × 19¹

Step-3: Factors of 27125

List of positive integer factors of 27125 that divides 27125 without a remainder.

1, 5, 7, 25, 31, 35, 125, 155, 175, 217, 775, 875, 1085, 3875, 5425

Step-4: Factors of 27132

List of positive integer factors of 27132 that divides 27125 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 19, 21, 28, 34, 38, 42, 51, 57, 68, 76, 84, 102, 114, 119, 133, 204, 228, 238, 266, 323, 357, 399, 476, 532, 646, 714, 798, 969, 1292, 1428, 1596, 1938, 2261, 3876, 4522, 6783, 9044, 13566

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27125 and 27132. The biggest common factor number is the GCF number.
So the greatest common factor 27125 and 27132 is 7.

Also check out the Least Common Multiple of 27125 and 27132